On the positivity of some bilinear functionals in Sobolev spaces

The positivity of a bilinear functional aa(f,g)=∑Nm=0λmC(m)(fm,gm) is studied as a function of coefficients λm. The concerned cases are those of Laguerre, Gegenbauer and Jacobi for c(m) = c(0), m = 1,…,N. The domain λmm=1N where a is positive definite, is given. As a consequence, when N = 1, the corresponding Markov-Bernstein inequalities are given.